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MP: Theoretische und Mathematische Grundlagen der Physik

MP 2: Symmetrien,Integrabilit
ät und Quantisierung

MP 2.1: Fachvortrag

Montag, 15. März 2004, 14:00–14:25, SR 2203

Group branching rules obtained from Hopf algebra cohomology of symmetric functions — •Bertfried Fauser¹ and Peter D. Jarvis² — ¹MPI Leipzig, Inselstrasse 22, D-04103 Leipzig — ²University of Tasmania, Hobart, TAS, Australia

Group branching laws are of great importance in various applications of group theory. We use the theory of symmetric functions to study such branching rules. Symmetric functions for a well recognized Hopf algebra which allows us to use Hopf algebra cohomology to classify one- and two cochains and cocylces. From these cocycles we construct branching operators, which allow to give closed formulae for the branching laws of unitary, orthogonal and symplectic groups. The method is close to quantum field theory applications and allows for a straight forward generalization to braided categories etc. Hence, a deep structural insight into a multitude of symmetries of physical systems is obtained. The talk is based on (math-ph/0308043).